spyrit.misc.walsh_hadamard.walsh_torch

spyrit.misc.walsh_hadamard.walsh_torch(x, H=None)

Return 1D Walsh-ordered Hadamard transform of a signal

Args:

x (torch.tensor): Input signals with shape (*, n).

H (torch.tensor, optional): 1D Walsh-ordered Hadamard matrix with shape (*, m).

Returns:

torch.tensor: Hadamard transformed signals with shape (*, m).

Note:

Providing the input argument H leads to much faster computation when multiple Hadamard transforms are repeated (see Example 2).

Example 1:

Sequency-ordered (i.e., Walsh) Hadamard transform

>>> import torch
>>> import spyrit.misc.walsh_hadamard as wh
>>> x = torch.tensor([1.0, 3.0, 0.0, -1.0, 7.0, 5.0, 1.0, -2.0])
>>> y = wh.fwht_torch(x)
>>> print(y)
>>> y = wh.walsh_torch(x)
>>> print(y)

Example 2:

Fast vs regular: Computation times for 5 batches of 512 signals of length 2**10

>>> import timeit
>>> import torch
>>> import numpy as np
>>> import spyrit.misc.walsh_hadamard as wh
>>> x = torch.rand(5, 1, 512, 2**10)
>>> t = timeit.timeit(lambda: wh.fwht_torch(x), number=200)
>>> print(f"Fast Hadamard transform (200x): {t:.4f} seconds")
>>> t = timeit.timeit(lambda: torch.from_numpy(walsh_matrix(x.shape[-1]).astype('float32')), number=200)
>>> print(f"Construction of Hadamard matrix (200x): {t:.4f} seconds")
>>> H = torch.from_numpy(walsh_matrix(x.shape[-1]).astype('float32'))
>>> t = timeit.timeit(lambda: wh.walsh_torch(x, H), number=200)
>>> print(f"Matrix-vector products (200x): {t:.4f} seconds")

Example 3:

CPU vs GPU: Computation times for 5 batches of 512 signals of length 2**10

>>> import timeit
>>> import torch
>>> import spyrit.misc.walsh_hadamard as wh
>>> x = torch.rand(5, 1, 512, 2**10)
>>> H = torch.tensor(walsh_matrix(x.shape[-1]), dtype=torch.float32)
>>> t = timeit.timeit(lambda: wh.walsh_torch(x, H), number=200)
>>> print(f"Fast Hadamard transform pytorch CPU (200x): {t:.4f} seconds")
>>> x = x.to(torch.device('cuda:0'))
>>> H = H.to(torch.device('cuda:0'))
>>> t = timeit.timeit(lambda: wh.walsh_torch(x, H), number=200)
>>> print(f"Fast Hadamard transform pytorch GPU (200x): {t:.4f} seconds")